BAGHDAD -- Budget battles are the latest roadblock delaying a decision by Baghdad on how many U.S. troops it might request stay in Iraq, although a top government official predicted Tuesday that the American military will remain as a training force beyond a year-end departure deadline.

Deputy Prime Minister Hussain al-Shahristani said there's no way to estimate how many troops would be asked to stay, or what exactly they will be doing, until parliament passes its $110 billion spending plan for 2012.

Iraq's Cabinet could tentatively sign off on the budget as early as next week, but parliament has until the end of the year to approve it.

"We are on a very tight budget," al-Shahristani said. But once the spending plan is settled, "then the Cabinet, and then I expect also the parliament, will approve that training program along with the purchase of the equipment."

Despite the delays, the comments by al-Shahristani, a major figure in Iraq's Shiite political leadership, were one of the most certain signs yet that Baghdad has decided to seek some sort of U.S. presence, likely numbering several thousand.

With about three months before the deadline, U.S. leaders are increasingly agitated with Iraq's reluctance to say whether it will ask U.S. troops to stay beyond the Dec. 31 departure date required by a 2008 security agreement between Washington and Baghdad.

Iraqi officials have been torn between their needs for U.S. help in security and public pressure for the Americans to leave, particularly from Shiite militants who threaten violence if they stay.

There are currently 44,500 U.S. troops in Iraq, due to fall to 40,000 by the end of the month, according to U.S. Joint Chiefs of Staff Chairman Mike Mullen. Starting in October, an estimated 1,000 troops will leave daily.

American officials said Iraq's government has not told them exactly what a continued U.S. military presence would do.

Al-Shahristani said one task American troops won't be asked to continue is joint patrols with Iraqi forces.

"We are very confident that we have enough trained forces in the country to deal with any terrorist activities or disturbances in Iraq," he said.

But he called it "extremely important" that Americans help in a training program, particularly for Iraq's nascent air and naval forces to protect its airspace and oil terminals in the Gulf.

The mission's size would depend in part on Iraqi defense purchases, including billions of dollars worth of fighter jets and patrol ships Iraq is buying from American manufacturers.